A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of 3?
A) 1
B) 15
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$

Question

A fair spinner has regions numbered 1 through 18. What is the probability that the spinner will stop on an even number or a multiple of 3? 
A) 1
B) 15
C) $\frac { 1 } { 3 }$
D) $\frac { 2 } { 3 }$

Quizplus · Accepted Answer

The even numbers between 1 and 18 are 2, 4, 6, 8, 10, 12, 14, 16, and 18 (9 in total). The multiples of 3 are 3, 6, 9, 12, 15, and 18 (6 in total). However, 6, 12, and 18 are both even and multiples of 3, so they should not be double-counted. Thus, there are 9 (even numbers) + 3 (additional multiples of 3 not already counted as even) = 12 favorable outcomes out of 18 possible outcomes, giving a probability of $\frac{12}{18} = \frac{2}{3}$.

A Fair Spinner Has Regions Numbered 1 Through 18 13\frac { 1 } { 3 }31​

A Fair Spinner Has Regions Numbered 1 Through 18 $\frac { 1 } { 3 }$